Finite coupling effects in double quantum dots near equilibrium

TL;DR

This paper evaluates a novel analytic continuation approach for quantum master equations, demonstrating its accuracy near equilibrium in double quantum dot systems and exploring effects of strong Coulomb interactions.

Contribution

It applies an analytic continuation method to fermionic systems, showing its validity near equilibrium and analyzing Coulomb effects in double quantum dots.

Findings

Method is accurate near equilibrium in fermionic systems.

Comparison shows Redfield methods are less accurate across regimes.

Strong Coulomb interactions influence system dynamics significantly.

Abstract

A weak coupling quantum master equation provides reliable steady-state results only in the van Hove limit, i.e., when the system-lead coupling approaches zero. Recently, J. Thingna et al. [Phys. Rev. E 88, 052127 (2013)] proposed an alternative approach, based on an analytic continuation of the Redfield solution, to evaluate the reduced density matrix up to second order in the system-bath coupling. The approach provides accurate results for harmonic oscillator and spin-bosonic systems. We apply this approach to study fermionic systems and the calculation on an exactly solvable double quantum dot system shows that the method is rigorously valid only near equilibrium, i.e., linear response regime. We further compare to the Redfield and the secular Redfield (Lindblad-type) master equations that are inaccurate in all parameter regimes. Lastly, we consider the non-trivial problem of strong Coulomb interaction and illustrate the interplay between system-lead coupling, inter-dot tunneling, and Coulomb strength that can be captured only via the analytic continuation method.